Flexural rotation capacity models fitted to test results using different statistical approaches

Abstract

Practical models for the ultimate deformations of flexure-controlled members were fitted to a database of thousands of tests. They cover beams, rectangular columns or walls, members with T-, H-, C-, or box section, conforming or not to seismic design codes, with or without fiber reinforced polymer jackets, in monotonic or cyclic uniaxial flexure with axial force. Model parameters were statistically derived assigning to each test (a) a weight of unity; (b) weight inversely proportional to the number of tests in a testing campaign, or (c) weight inversely proportional to the root-meansquare error of tests in a campaign. Predictions correlate well to those of a physical model based on curvatures and a plastic hinge length. Analysis of variance suggests that the scatter of model predictions with respect to test results comes more from the testing itself than from the model. Intralab and interlab variabilities are quantified and pure error is estimated from tests of nominally identical specimens.

Cyclic shear resistance for seismic design, based on monotonic shear models in fib Model Code 2010 and in the 2018 draft of Eurocode 2

“…3. Grammatikou et al 13,14 give expressions for ϑ y and ϑ u of rectangular beams, columns or walls, circular columns, nonrectangular walls and members with box section, which agree well with thousands of cyclic tests of flexure-critical members of these types.…”

“…Table shows that the new model does better in classifying correctly the failure mode of flexure‐critical members than the Biskinis et al model, despite the smaller prediction scatter of the latter. Note that the models in Grammatikou et al for the cyclic flexural deformation capacity of the flexure‐critical specimens in Table misclassify as flexure‐critical 10.8% of the shear‐critical specimens in Tables and .…”

“…The variances of the natural logs of the test‐to‐model ratios and their covariance are: …”

“…Finally, the new proposal was applied to estimate the cyclic shear resistance of a large number of specimens with ribbed (deformed) bars which failed in flexure under cyclic loading. 13,14 If the estimated shear resistance-at the ductility factor corresponding to the experimental ultimate deformation in flexure-is less than the shear force corresponding to the experimental yield moment, the cyclic shear resistance model leads to the false prediction that the member fails in shear, instead of flexure. Table 9 shows that the new model does better in classifying correctly the failure mode of flexure-critical members than the Biskinis et al 18 model, despite the smaller prediction scatter of the latter.…”

“…Their shear resistance, V R , was computed for the inclination θ that gives V R = V R,s (+V R,c ) = V R,max , with ε x computed by applying Equation (6) to the test specimen's end section, for a moment equal to M = V R L s . The experimental resistance was taken equal to the shear force at ultimate deformation, conventionally identified with the point where the lateral force resistance (i.e., the applied shear) drops by at least 20% with respect to the peak resistance reached before (Biskinis and Fardis, 10,11 Grammatikou et al [12][13][14]. Figure 2 compares the experimental cyclic shear resistance to the MC2010 predictions and Table 3 gives the median and the coefficient of variation (cov) of the testto-model ratios.…”